Painters, even the most experimental ones, continually time-travel for inspiration. Right now, you can traverse half a millennium of painting within two dozen blocks on the Upper East Side.

Begin with a conclave of panels by Piero della Francesca, painted between the years 1454 and 1470. (Frick Collection, 1 East 70th Street, 212-288-0700, frick.org. Through May 19.) Along with other early-Renaissance painters, Piero (ca. 1412–1492) worked through the rigid Christian symbolism of the Middle Ages to rediscover the humanistic forms of the ancient Greeks. He surrounded his saints with the naturalistic light and space that has been the body and blood of painting ever since, even for artists such as Kazimir Malevich, who rejected the "dictatorship" of representation in his flat Suprematist squares and yet still wanted "to extract from the works of the great masters the feeling expressed."

The sculptural majesty of Piero's figures stems partly from his quest to capture the most fleeting nuances of natural light across every surface, whether flesh or stone. In the three-and-a-half-foot-tall Virgin and Child Enthroned With Four Angels, a row of carved marble rosettes under Mary's feet shifts from warm white to ash gray as that light waxes and wanes; two decorative reliefs—one shaded, the other in raking light—form a sophisticated negative/positive frame for the Virgin's exquisitely modeled head. Geometric pink and blue angels' wings and walls expressed as flat black and red rectangles reveal that enhancing reality through pure abstraction is an ancient trick.

Next, transport yourself to the Baroque era through the 1639 Portrait of Duke Francesco I d'Este by Velázquez (1599–1660). (Metropolitan Museum of Art, 1000 Fifth Avenue, 212-535-7710, metmuseum.org. Through July 14.) Perhaps no other artist in history makes the alchemy of painting—multiple perceptions entering the artist's eyes, interpreted by the mind and combined with the physical application of pigments to a flat surface—look as effortless as Velázquez. If Piero's Madonna has a spiritual serenity, Velázquez's Duke will suffer no fools.

Of course, clad anyone in armor and a magenta cloak and a certain gravitas will obtain, but the Duke, who began ruling his small Italian state in his teens, meets our gaze with somber eyes that have already witnessed many battles and the shifting alliances of the Thirty Years' War. It is a young face, with a sparse mustache shadowing a drained smile; two centuries later, a photograph would undoubtedly have captured many more—and superfluous—details. But a portrait such as this is built up from thousands of the artist's glances segueing between subject and canvas, which generate minute decisions of the hand—evidence of lived experience, of time passing, that no photograph can hope to match.

Still, artist and royal were both busy, and one courtier reported back to Italy from Spain, "Velázquez is making the portrait of your highness, which will be marvelous. However, like other men of talent, he has the defect of never finishing and of not telling the truth." Possibly, but even when Velázquez strokes quick highlights onto the armor or gathers the cloak in bursts of compositional tension, he never loses touch with the body before him. If Piero's luminous solemnity can be seen 500 years later in Morandi's mesmerizing still lifes, Velázquez's physical vigor lives on in de Kooning's ferocious women.

Now trudge back down Fifth Avenue to wearily contemplate what the paintings of Elizabeth Peyton might beget, come the year 2525. The dilettante's Warhol, Peyton (b. 1965) specializes in portraits of the zeitgeist—she's cranked out images of celebs as disparate as Sid Vicious and Michelle Obama. "Klara 13 Pictures" focuses mainly on depictions of the artist Klara Liden, created between 2009 and 2012. (Michael Werner, 4 East 77th Street, 212-988-1623, michaelwerner.com. Through June 15.) The works here are purged of the loud colors Peyton has often deployed to punch up the pictures of sullen pop stars she cribs from mass media. Instead, we get Klara's sketchily modeled pink head topping her bulkily outlined body. Neither fish nor fowl, the images convey none of the accreted visual heft of good painting or the immediate graphic verve of strong illustration. The best moments, such as translucent waves of hair gathering in brushy jags, ultimately come off as mannered technique.

In a 10-by-8-inch image of a glass filled with flowers set against a mottled background, Peyton attempts to generate conceptual mojo by cropping some of the blooms, emphasizing the ragged edges of the support panel. Perhaps a meditation on how volumetric reality must, of necessity, endure the harsh limits of two-dimensional representation, this tin-eyed composition suffers from lazily painted petals congealing beneath a muddy light source.Maybe these bland, throwaway images are simply the painting our age of iPhone snapshots deserves.

Then again, Albert York died only four years ago, and his paintings, as small as Peyton's but much more genuinely intimate, offer future generations a powerful alternative to cack-handed ennui.

The painted flowers on view in "Albert York: A Loan Exhibition" (Davis & Langdale, 231 East 60th Street, 212-838-0333, through June 14) are observed through a scrim of struggle—scraped out, repainted, and laboriously layered individual petals suddenly coalesce into quirkily balanced fans of color. In his landscapes, York's figures often seem eccentrically posed, and yet the way the curve of a knee echoes the hollow of a dog's throat lends one bucolic scene a magisterial expansion, something akin to continental drift wrenching South America out of Africa.

York conveys an offhand weirdness—a skeleton sits cross-legged in a yard, flattering a nude woman; outsize snakes squiggle across green-and-brown lawns, suggestive of changing seasons, that eternal churn of life. York once told an interviewer we live in a Garden of Eden: "It might be the only paradise we ever know, and it's just so beautiful, with the trees and everything here, and you feel you want to paint it."